{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "source": [
    "import tensorflow as tf\r\n",
    "tf.__version__"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "'2.6.0'"
      ]
     },
     "metadata": {},
     "execution_count": 1
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "source": [
    "def sigmoid(x):\r\n",
    "    s=1/(1+tf.math.exp(-x))\r\n",
    "    return s"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "source": [
    "from matplotlib import pyplot as plt\r\n",
    "%matplotlib inline\r\n",
    "\r\n",
    "x=tf.linspace(-10.0,10.0,100)\r\n",
    "plt.plot(x,sigmoid(x))"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aed9db0460>]"
      ]
     },
     "metadata": {},
     "execution_count": 7
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "source": [
    "def sigmoid_derivative(x):\r\n",
    "    d_s=sigmoid(x)*(1-sigmoid(x))\r\n",
    "    return d_s"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "source": [
    "x= tf.Variable(x)\r\n",
    "with tf.GradientTape() as tape:\r\n",
    "    s=1/(1+tf.math.exp(-x))\r\n",
    "    \r\n",
    "    \r\n",
    "grad = tape.gradient(s,x)\r\n",
    "grad"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(100,), dtype=float32, numpy=\n",
       "array([4.53958128e-05, 5.55575862e-05, 6.79936929e-05, 8.32131336e-05,\n",
       "       1.01838428e-04, 1.24631639e-04, 1.52524692e-04, 1.86658130e-04,\n",
       "       2.28426594e-04, 2.79536616e-04, 3.42074229e-04, 4.18591371e-04,\n",
       "       5.12206519e-04, 6.26731722e-04, 7.66824465e-04, 9.38173209e-04,\n",
       "       1.14772201e-03, 1.40394329e-03, 1.71716651e-03, 2.09997571e-03,\n",
       "       2.56768288e-03, 3.13889817e-03, 3.83620127e-03, 4.68693674e-03,\n",
       "       5.72414091e-03, 6.98759547e-03, 8.52504466e-03, 1.03935143e-02,\n",
       "       1.26607250e-02, 1.54065182e-02, 1.87241677e-02, 2.27213893e-02,\n",
       "       2.75206938e-02, 3.32587175e-02, 4.00838554e-02, 4.81513925e-02,\n",
       "       5.76152131e-02, 6.86149076e-02, 8.12573582e-02, 9.55919623e-02,\n",
       "       1.11580029e-01, 1.29060090e-01, 1.47712946e-01, 1.67034864e-01,\n",
       "       1.86326414e-01, 2.04710141e-01, 2.21183687e-01, 2.34711796e-01,\n",
       "       2.44347483e-01, 2.49363437e-01, 2.49363378e-01, 2.44347528e-01,\n",
       "       2.34711781e-01, 2.21183747e-01, 2.04710126e-01, 1.86326474e-01,\n",
       "       1.67034894e-01, 1.47713035e-01, 1.29060090e-01, 1.11580126e-01,\n",
       "       9.55919847e-02, 8.12574103e-02, 6.86149448e-02, 5.76152541e-02,\n",
       "       4.81514111e-02, 4.00838554e-02, 3.32587361e-02, 2.75206920e-02,\n",
       "       2.27213968e-02, 1.87241696e-02, 1.54065238e-02, 1.26607250e-02,\n",
       "       1.03935199e-02, 8.52504466e-03, 6.98759919e-03, 5.72414091e-03,\n",
       "       4.68694093e-03, 3.83620267e-03, 3.13890073e-03, 2.56768381e-03,\n",
       "       2.09997781e-03, 1.71716756e-03, 1.40394329e-03, 1.14772131e-03,\n",
       "       9.38174082e-04, 7.66824989e-04, 6.26731780e-04, 5.12206287e-04,\n",
       "       4.18591808e-04, 3.42074578e-04, 2.79536616e-04, 2.28426608e-04,\n",
       "       1.86658348e-04, 1.52524823e-04, 1.24631639e-04, 1.01838443e-04,\n",
       "       8.32130463e-05, 6.79937657e-05, 5.55575898e-05, 4.53958055e-05],\n",
       "      dtype=float32)>"
      ]
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "source": [
    "plt.plot(x.numpy(),grad.numpy())"
   ],
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1aed9e4f0a0>]"
      ]
     },
     "metadata": {},
     "execution_count": 11
    },
    {
     "output_type": "display_data",
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ],
      "image/svg+xml": "<?xml version=\"1.0\" encoding=\"utf-8\" standalone=\"no\"?>\r\n<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\r\n  \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\r\n<svg height=\"248.518125pt\" version=\"1.1\" viewBox=\"0 0 378.465625 248.518125\" width=\"378.465625pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\r\n <metadata>\r\n  <rdf:RDF xmlns:cc=\"http://creativecommons.org/ns#\" xmlns:dc=\"http://purl.org/dc/elements/1.1/\" xmlns:rdf=\"http://www.w3.org/1999/02/22-rdf-syntax-ns#\">\r\n   <cc:Work>\r\n    <dc:type rdf:resource=\"http://purl.org/dc/dcmitype/StillImage\"/>\r\n    <dc:date>2021-08-17T16:19:42.961063</dc:date>\r\n    <dc:format>image/svg+xml</dc:format>\r\n    <dc:creator>\r\n     <cc:Agent>\r\n      <dc:title>Matplotlib v3.4.3, https://matplotlib.org/</dc:title>\r\n     </cc:Agent>\r\n    </dc:creator>\r\n   </cc:Work>\r\n  </rdf:RDF>\r\n </metadata>\r\n <defs>\r\n  <style 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"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "source": [],
   "outputs": [],
   "metadata": {}
  }
 ],
 "metadata": {
  "orig_nbformat": 4,
  "language_info": {
   "name": "python",
   "version": "3.9.6",
   "mimetype": "text/x-python",
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "pygments_lexer": "ipython3",
   "nbconvert_exporter": "python",
   "file_extension": ".py"
  },
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3.9.6 64-bit"
  },
  "interpreter": {
   "hash": "25bf1dab56f13e21d80318cd5e789e076f92a14fa9924f370a2a818164c863f4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}